US7774041B2 - Method and apparatus for calculating index concerning local blood flow circulations - Google Patents
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Definitions
- the present invention relates to a calculation method and apparatus of an index concerning local blood flow circulations in cerebral tissues.
- configuration information from a simple CT image, and circulation information of blood flow around a seat of disease in a dynamic scan by contrast CT can be obtained as visual information.
- a high-speed scan by multislice CT has been possible and it is considered that a utilization range of the dynamic scan of contrast CT is increasingly enlarged.
- the CBP study comprises: obtaining indices such as CBP, CBV, MTT, and Err quantitatively indicating local blood flow circulations in the tissues, that is, the circulations of the blood flow through the capillaries in the local tissues; and outputting maps of these indices.
- CBP denotes blood flow rate [ml/100 ml/min] per unit volume and time in the capillaries for the cerebral tissues
- CBV denotes a blood volume [ml/100 ml] per unit volume in the cerebral tissues
- MTT denotes a blood mean transit time [second] of the capillaries
- Err denotes a sum of residual errors or square root of the sum of squares of the residual errors in approximation of a modulation transfer function.
- the indices CBP, CBV, MTT quantitatively indicating the blood flow circulations of the capillaries in the cerebral tissues, together with transit time information after development of cerebral ischemia apoplexy, are expected as useful information for differentiating a disease body of ischemic cerebral vascular disorder, judging the presence/absence of enlargement of the capillaries, or evaluating blood flow rate.
- ischemic cerebral vascular disorders blood pressure of a provided artery drops, and the intravascular blood flow rate drops.
- MTT extends, and CBP drops.
- a contrast medium having no cerebral vessel permeability such as an iodinated contrast medium
- the iodinated contrast medium is injected via a cubital vein, for example, by an injector.
- the iodinated contrast medium injected into the vein by the injector flows into a cerebral artery via heart and lung. Then, the contrast medium flows out to the cerebral veins from the cerebral arteries through the capillaries in the cerebral tissues.
- the iodinated contrast medium passes through the capillaries in normal cerebral tissues without any extravascular leakage.
- FIG. 1 schematically shows this state.
- the state of passage of the contrast medium is scanned by dynamic CT, and a time-density curve Ca(t) of a pixel on the cerebral artery, time-density curve Ci(t) of the pixel on the cerebral tissue (capillary), and time-density curve Csss(t) of the pixel on the cerebral vein are measured from a continuous image.
- the time-density curve Ca(t) of the cerebral artery is used as an input function
- the time-density curve Ci(t) for the cerebral tissue is used as an output function
- a modulation transfer function between the input and output functions is approximated by a rectangular function.
- the modulation transfer function indicates a process of passage of the tracer through the capillary.
- the CBP study has the following problems.
- an image using the value as the pixel value can be constituted, and this image is referred to as a map.
- R maps can be constituted.
- This vector value map V k is prepared for each time-density curve Ca(t) k of the referred cerebral artery.
- the time-density curves of the cerebral arteries are obtained from medial, anterior and posterior cerebral arteries in left and right hemispheres.
- the CBP study also has the following problems.
- bolus injection via the cubital vein for a contrast enhancement effect observed with the CT, the CT number of blood rises to several hundreds of HU at maximum (several tens of HU, when contrast imaging is not performed).
- a contrast enhancement effect has to be measured only with an error of several percentages or less. That is, even when the contrast enhancement effect (the rise of CT number) is about 20 to 40 HU, the contrast enhancement effect has to be detected.
- a standard deviation (sd) of noise is in inverse proportion to a square root of an X ray radiation dose, and sd is, for example, about 5 to 10 HU in typical irradiation conditions. Therefore, to detect the contrast enhancement effect of 0.5 HU, the X ray radiation dose has to be increased by about 10 to 100 times, and this means that an exposed dose of a patient is remarkably large. Moreover, since the same position is scanned several tens of times in the dynamic CT, exposure of skin in the scanned position reaches several hundreds to thousands of times the normal exposure, and this is not realistic in consideration of radiation troubles such as inflammation, alopecia, necrosis, and carcinogenesis.
- the X ray radiation dose has to be decreased as compared with the usual scanning.
- the X ray radiation dose per scan is reduced, for example, to about 1 ⁇ 2 to 1/10 of a usual dose.
- sd is, for example, about 15 to 20 HU, and the contrast enhancement effect of about 0.5 to 1.5 HU can hardly be detected.
- the slice thickness is set to be large during the scan, or the number of images of continuous thin slices is averaged and the image of a thick slice is generated. Since the X ray radiation dose per pixel increases in proportion to the slice thickness, sd of the image noise decreases in inverse proportion to the square root of the slice thickness. However, when the slice thickness is increased, a partial volume effect is produced. That is, one pixel does not show a uniform cerebral tissue, a probability that the pixel shows the mean CT number of a plurality of tissues (white matter, gray matter, blood vessel, cerebral sulci, cerebral ventricles, and the like) is incorrect, and the value of the cerebral blood flow rate obtained as the analysis result becomes incorrect.
- n about 2 to 4 is a limitation, and a sufficient noise suppressing effect cannot be obtained only with this measure.
- the smoothing has to be only slightly performed.
- it is important to remarkably reduce the size of the image filter for example, to about 3 ⁇ 3.
- the time resolution is remarkably impaired.
- the dynamic CT is originally performed in order to obtain a high time resolution by performing scanning in a short sampling cycle and to precisely measure a slight and rapid change (degree of a smoothing effect resulting particularly from a physiologic structure) of the time-density curve, and the smoothing with time is not appropriate.
- Another object of the present invention is to suppress noise without decrease of spatial and time resolution, and thereby enhance an analysis precision of the CBP study.
- FIG. 1 is a principle explanatory view of a CBP study
- FIG. 2 is a block diagram showing a constitution of an index calculation apparatus concerning blood flow circulations of capillaries in cerebral tissues according to an embodiment of the present invention
- FIGS. 3A , 3 B, 3 C are explanatory views of an image processing by a coherent filter of the present embodiment
- FIGS. 4A , 4 B are flowcharts showing a flow of noise suppressing processing by the coherent filter in the present embodiment
- FIG. 5 is a flowchart of a former half of a whole index calculation processing in the present embodiment
- FIG. 6 is a flowchart of a latter half of the whole index calculation processing in the present embodiment.
- FIG. 7 is a diagram showing one example of a dividing line of step S 3 of FIG. 5 ;
- FIG. 8 is a diagram showing an influence range of each cerebral artery on Voronoy diagram for use in decreasing the number of processing steps of step S 12 of FIG. 6 ;
- FIGS. 9A , 9 B, 9 C are diagrams showing AT, PT, and TT maps of step S 4 of FIG. 5 ;
- FIG. 10 is a diagram showing AT, PT, TT of the step S 4 of FIG. 5 ;
- FIG. 11 is a diagram showing a cerebral artery ROI which is common among slices in step S 6 of FIG. 5 ;
- FIG. 12 is a diagram showing an upper sagittal sinus venosus ROI set in step S 7 of FIG. 5 ;
- FIG. 13 is a supplementary diagram concerning correction of a time-density curve of the cerebral artery of step S 10 of FIG. 5 ;
- FIGS. 14A , 14 B show one example of a time-density curve Ca(t) of the cerebral artery and time-density curve Ci(t) for the cerebral tissue prepared in steps S 10 , S 11 of FIG. 5 ;
- FIG. 15 is a principle explanatory view of a box-MTF method of step S 12 of FIG. 6 ;
- FIG. 16 is an explanatory view of a box-MTF processing of the step S 12 of FIG. 6 ;
- FIG. 17 is a diagram showing one example of an output range setting screen of each index of step S 14 of FIG. 6 ;
- FIGS. 18A to 18D are diagrams showing one example of each map of CBP, CBV, MTT, Err prepared in step S 16 of FIG. 6 ;
- FIG. 19 is a diagram showing a list of the CBP, CBV, MTT, and Err maps prepared for each cerebral artery in the step S 16 of FIG. 6 ;
- FIG. 20 is an explanatory view of a map synthesis method of step S 17 of FIG. 6 ;
- FIGS. 21A to 21D are diagrams showing display examples of a mean value calculated in step S 19 of FIG. 6 ;
- FIG. 22 is a diagram showing a generation method of a map (control map) in which cerebral arteries (ACA, MCA, PCA) having a high dominance possibility are distinguished by labels for each pixel (local tissue) in the step S 17 of FIG. 6 ;
- FIG. 23 is a diagram showing an example of the control map generated by the generation method of FIG. 22 ;
- FIGS. 24A to 24C are diagrams showing the CBP map filtered using the control map.
- Characteristics of the present embodiment lie in a method of: synthesizing many index maps generated by a CBP study into one map, so that diagnosis efficiency of the CBP study is enhanced; and further using a coherent filter to establish both reduction of noise and inhibition of drop of space and time resolutions so that precision of an index is enhanced.
- the present embodiment relates to a method and apparatus in which an index indicating a local blood flow circulation is calculated from a plurality of images concerning a specific region of a subject and continuous with time, and a modality generating the plurality of images as objects is not limited to a specific apparatus.
- the apparatus include an X-ray computer tomography apparatus (X-ray CT apparatus), single photon emission tomography apparatus (SPECT), positron emission tomography apparatus (PET), and magnetic resonance imaging apparatus (MRI).
- X-ray CT apparatus single photon emission tomography apparatus
- PET positron emission tomography apparatus
- MRI magnetic resonance imaging apparatus
- FIG. 2 shows a constitution of the X-ray CT apparatus according to the present embodiment.
- the X-ray CT apparatus is constituted of a gantry section 10 and computer apparatus 20 .
- the gantry section 10 includes an X-ray tube 101 , high voltage generation apparatus 101 a , X-ray detector 102 , and data acquisition system (DAS) 103 .
- the X-ray tube 101 and X-ray detector 102 are disposed opposite to each other via a subject P on a rotary ring (not shown) which continuously rotates at a high speed.
- the computer apparatus 20 includes an image processing apparatus 30 , image display section 107 , and input section 109 .
- the image processing apparatus 30 includes a control section 108 as a central unit, and further includes: a preprocessing section 104 for converting raw data output from the data acquisition system 103 to projection data through a correction processing; a memory section 105 for storing the projection data; an image reconstitution section 106 for reconstituting CT image data from the projection data; a storage apparatus 10 M for storing the CT image data; a coherent filter processing section 110 for executing a coherent filter processing with respect to the CT image data; and a CBP study processing section 120 for using the CT image data subjected to the coherent filter processing to execute a CBP study processing.
- the coherent filter processing section 110 includes a dispersed value estimation section 111 , weight function calculation section 112 , and pixel value calculation section (coherent filter section) 113 . Functions of these dispersed value estimation section 111 , weight function calculation section 112 , and pixel value calculation section 113 will be described hereinafter in detailed description of a coherent filter processing.
- the CBP study processing section 120 includes an ROI setting support section 121 , time-density curve preparation section 122 , cerebral artery time-density curve correction section 123 , MTF processing section 124 , index calculation section 125 , map preparation section 126 , and map synthesis section 127 .
- the ROI setting support section 121 prepares and provides information (AT, PT, and TT maps for a cerebral artery ROI) for supporting an operation to set a region of interest ROI with respect to cerebral artery and vein on an CT image.
- the cerebral artery ROI is separately set in regions of left and right brain, for example, with respect to an anterior cerebral artery (ACA), medial cerebral artery (MCA), and posterior cerebral artery (PCA) as objects. Therefore, in this example, three for each side, that is, six cerebral artery ROI in total are set.
- ACA anterior cerebral artery
- MCA medial cerebral artery
- PCA posterior cerebral artery
- three for each side that is, six cerebral artery ROI in total are set.
- another time-density curve Csss(t) is used in order to correct a time-density curve Ca(t) of the cerebral artery.
- This time-density curve Csss(t) is prepared with respect to the ROI set on a sufficiently thick vessel in which a pixel not including a partial volume exists.
- ROI of Csss(t) is set, for example, in a thickest upper sagittal sinus venosus in cerebral vessels.
- the time-density curve preparation section 122 prepares the time-density curve concerning the cerebral artery, cerebral vein, and cerebral tissue (capillary) from dynamic CT image data (a plurality of image data continuous with time) stored in the storage apparatus 10 M. Moreover, the time-density curve Ca(t) of the cerebral artery is separately prepared, for example, for each of six set cerebral artery ROIs. The time-density curve Csss(t) of the cerebral vein is prepared with respect to the cerebral vein ROI set in the upper sagittal sinus venosus. Moreover, the time-density curve Ci(t) for the cerebral tissue is prepared for each of all pixels on the cerebral tissue as objects.
- the cerebral artery time-density curve correction section 123 corrects the time-density curve Ca(t) of the cerebral artery based on the time-density curve Csss(t) of the upper sagittal sinus venosus.
- the correction method will be described later.
- the MTF processing section 124 calculates a modulation transfer function MTF for each of all the pixels in a cerebral tissue region as objects based on the corrected time-density curve Ca(t) of the cerebral artery and time-density curve Ci(t) for the cerebral tissue by a box-MTF method.
- An index calculation section 125 calculates indices (CBP, CBV, MTT, Err) indicating blood flow circulations from the calculated modulation transfer function MTF for each of all the pixels in the cerebral tissue region as the objects.
- the map synthesis section 127 is disposed in order to reduce the enormous number of maps by synthesis processing and enhance diagnosis efficiency.
- a principle of the coherent filter will briefly be described. For example, 3 ⁇ 3 local pixels in the vicinity are weighted-averaged, and this weighted average value is used as the value of a local center pixel. Weights of peripheral pixels are changed in accordance with similarity between the center pixel and peripheral pixel.
- the similarity is an index indicating a degree of possibility that the pixels are anatomically close tissues, concretely, cerebral tissues (capillaries) under control of the same cerebral artery.
- a high weight is given to a pixel having a high similarity, and conversely a low weight close to zero is given to a pixel having a low similarity, so that noise is suppressed, and drop of the spatial resolution can be inhibited.
- the similarity can appropriately be replaced with fidelity or risk rate.
- the brain of the subject into which a contrast medium having no cerebral vascular permeability, for example, an iodinated contrast medium is injected is used as a scanning object, and a plurality of continuously acquired CT images (dynamic CT images) are used to calculate the similarity by comparison of the time-density curves of the respective pixels. Therefore, certainty of the similarity depends on and is determined by a sampling frequency, the number of images per unit time, and sampling number, that is, the number of all images. Therefore, it is effective to reduce a scan interval, for example, to 0.5 second.
- a digital image acquired via scan means such as a camera and CT scanner is constituted of a plurality of pixels (or the image can be considered as a set of pixel).
- the position of the pixel is represented as a vector x (i.e., the vector of a coordinate value)
- the value of the pixel x i.e., a numeric value indicating shading, CT number HU
- the pixel x is a two-dimensional vector indicating a coordinate value (x,y) indicative of a position on the image.
- a “pixel value v(x)” defined with respect to a certain pixel x is represented as follows.
- v ( x ) ( v 1 ( x ), v 2 ( x ), . . . , v K ( x )) (1) wherein v 1 (x), v 2 (x), . . . , v K (x) in the right side of the equation (1) will hereinafter be referred to as “scalar values” with respect to the pixel x.
- the image is a dynamic image constituted of K still images
- the pixel of the n-th image has a scalar value v n (x)
- a set N(x) of appropriate peripheral pixels is considered with respect to the pixel x (this set N(x) may include the pixel x).
- a weight w(p(x,y)) of a peripheral pixel y as an element of N(x) with respect to a center pixel x is considered.
- This weight w(p(x,y)) has the following properties.
- this p(x,y) is means for quantifying the “similarity” mentioned in the present embodiment.
- this value indicates a concrete numeric value indicative of a degree of similarity between the center pixel x and peripheral pixel y ⁇ N(x) in some meaning (e.g., a degree of a statistical difference recognized between the pixel values v(x) and v(y) of both pixels x and y).
- p(x,y) indicating a large value
- a possibility that the pixels x and y have “no statistically significant difference (i.e., a high similarity)” and are similar to each other is judged to be high.
- p(x,y) indicating a small value
- the pixels x and y are judged to “have the statistically significant difference (i.e., low similarity)”.
- the pixel values v(x) and v(y) (or scalar values v 1 (x), . . . , v K (x) and v 1 (y), . . . , v K (y)) necessarily include noise.
- the noise generated by a dark current in the device and irregular fluctuation of light amount incident from an outer world exist in the respective pixels constituting the image.
- the function p(x,y) can be constituted as the risk rate (or a significant level), when the hypothesis H is rejected (in this case, p(x,y) is defined as a function such that a value range is [0, 1] (p(x, y) ⁇ [0, 1])).
- the weight w(p(x,y)), the weight w(p(x,y)) is a function of the risk rate p(x,y) as described above.
- the weight is a function of fidelity.
- the function can be constituted to be w(p(x,y)).
- a weight function w acting on the risk rate p(x,y) obtained with respect to combinations of x and y in order to obtain the weight w(p(x,y)) has an action of realizing the “rejection”.
- the weight function w i.e., the weight w(p(x,y)) indicates a large positive value.
- the function is adjusted to have a small positive value (or “0”).
- a concretely form of the weight function w will be described later. That is, when the pixels x and y satisfy the proposition indicated by the hypothesis H, the weight w(p(x,y)) indicates a large value. In the opposite case, the weight has a small value.
- particularly w may be constituted to indicate two values; “0”; and a constant value other than “0”.
- a relation among the above-described hypothesis H, risk rate p(x,y), and weight w(p(x,y)) will be summarized.
- a similarity p also increases, and a weight w given to the pixel is raised.
- the possibility that the null hypothesis H is correct is low, then the similarity p is low, and the weight w given to the pixel is lowered.
- contribution (weight) of the weighted average value is changed in accordance with the similarity in this manner, it is possible to inhibit the drop of the resolution and effectively suppress the noise.
- a weight function w(t) can be the to be a “positive/negative monotonous increase function defined by t ⁇ [0, 1]”, and the w(t) may satisfy at least the above-described properties.
- a “coherent filter” is derived as follows. That is, first the above-described weights w(p(x,y)) of all pixels y as elements of a set N(x) are calculated with respect to a certain pixel x constituting the image. Subsequently, these weights w(p(x,y)) are used to calculate a new scalar value v′ k (x) constituting the pixel x in the following equation (2).
- v ' ⁇ k ⁇ ( x ) ⁇ y ⁇ N ⁇ ( x ) ⁇ ⁇ v k ⁇ ( y ) ⁇ w ⁇ ( p ⁇ ( x , y ) ) ⁇ y ⁇ N ⁇ ( x ) ⁇ w ⁇ ( p ⁇ ( x , y ) ) ( 2 )
- k 1, 2, . . . , K.
- v′ k (x) obtained by this equation is used to constitute a converted pixel value (new pixel value) v′(x) of the pixel x as follows.
- v ′( x ) ( v′ 1 ( x ), v′ 2 ( x ), . . . , v′ K ( x )) (3)
- This processing can generally be the as follows. That is, when a plurality of pixels x constituting a certain image exist, fidelity p(x,y) of this pixel x with a certain arbitrary pixel y (y ⁇ N(x) was set in the above description) is quantized. When h above description) is quantized. When the fidelity is large, a large contribution of the pixel y is recognized in a weighted averaging processing using the pixel value v(y). When the fidelity is small, only the small contribution is recognized. Thereby, it can be the that the noise of the pixel x is effectively suppressed in an image processing method.
- the pixel y is allowed to further contribute to the averaging processing. In other words, when the pixels are “not similar to each other”, the pixel y is totally or almost ignored (the weight is set to zero or an approximate value).
- the use is not limited to noise suppression.
- the weight function, or the coherent filter is set in a preferable concrete form. Then, a superior effect can be fulfilled.
- the above-described “dynamic CT” scan is a scan system in which the X-ray tube 101 and X-ray detector 102 repeatedly photograph the same portion of the subject P (the repeated scan is often performed by continuous rotation in a repeated scan, and continuous rotary CT apparatus) to successively acquire projection data, a reconstitution processing is successively performed based on the projection data, and a time series of images are obtained.
- the image display in the image display section 107 is controlled, for example, by a counter (not shown), so that the display is performed a constant time after the scan start or end point for collecting the projection data as an original image.
- the image acquired/displayed in this manner is a so-called dynamic image including the time series of a plurality of still images similarly as in the movies.
- scan system is typically used to inject the contrast medium into the subject P, observe/analyze a change with an elapse of time, and analyze a pathological state of an affected area such as stenosis and occlusion in the vessel.
- a system of performing the CT scan of the same portion only twice before and after contrast medium administration can be considered as a broad dynamic CT scan.
- the image acquired by the dynamic CT scan is a dynamic image as described above, and scanned for a purpose of observing the change with time in detail. Therefore, the impairment of the time resolution cannot essentially be the to be a preferable situation.
- the following dynamic coherent filter processing can be carried out in which the time resolution is not impaired and the noise can be suppressed from all of K still images (a plurality of images).
- v ( x ) ( v 1 ( x ), v 2 ( x ), . . . , v K ( x )) (1)
- suffixes 1, 2, . . . , K in right-side terms are serial numerals of K still images.
- the set N(x) is assumed to be a set of pixels included in a rectangular peripheral area centering on the pixel x. More concretely, for example, for the set N(x) when 128 ⁇ 128 pixels in total constitute one noted still image, an area for 3 ⁇ 3 pixels centering on the pixel x is defined. Furthermore, when 512 ⁇ 512 pixels constitute the still image, an area for 13 ⁇ 13 pixels centering on the pixel x may be defined.
- ⁇ k in the above equation (4) is a standard deviation of the noise estimated on an assumption that each of k still images has a constant common degree of noise.
- C is an adjustable parameter which determines a degree of action with the weight wl(p(x,y)) assigned to the above equation (4).
- ⁇ k in the equation (4) will be described (hereinafter described as a dispersal ⁇ k 2 ).
- this ⁇ k 2 is a dispersal of noise component possessed by the scalar value of each pixel on k still images.
- the dispersal ⁇ k 2 in the above equation (4) is estimated on an assumption that the scalar value of each pixel of k images includes noise with a constant value of dispersal ⁇ k 2 . In general, this assumption has a sufficient validity in the following background.
- the noise of the CT image is determined by an X ray radiation dose, that is, a product of a tube current of the X-ray tube 101 in a proportional relation and an irradiation time (so-called current time product (mA ⁇ s)).
- a physical X-ray filter for adjusting the X ray radiation dose e.g., called a “wedge” or “X-ray filter” formed of a copper foil or solid metal blank
- the dispersal is therefore negligible.
- the wedge has a function of using a fact that the subject P is formed of a material substantially with the same density as that of water, and attenuating a part of the X ray radiation dose so that the same degree of X ray radiation dose is detected in any X-ray detector 102 . Therefore, according to the wedge, as a result, an effect is produced that the dispersal ⁇ k 2 of the noise has a substantially constant value regardless of the position of the pixel x.
- the wedge is disposed for an essential purpose of effectively using the dynamic range of the X-ray detector 102 .
- the dispersal ⁇ k 2 is substantially constant with respect to all pixels on k still images in K still images acquired by the dynamic CT scan.
- the present embodiment is extended for the dispersal different with each pixel.
- the radiation dose (X-ray tube current x radiation time (mAs)) may be changed every scan.
- the dispersal ⁇ k 2 differs with each image in this case.
- ⁇ k 2 ⁇ ⁇ ⁇ k 0 2 ⁇ R k R k ⁇ ⁇ 0 ( 5 )
- the concrete numeric value of ⁇ k 2 can be estimated with respect to at least one k by the following method.
- N (1 ⁇ N ⁇ K) images which can be assumed to hardly have a change in the subject P in K scan operations and obtaining an anticipated value E[ ⁇ k 2 ] with respect to the dispersal ⁇ k 2 by actual measurement is effective.
- v K (x f ) constituting the pixel value v(x f ) of a certain pixel x f in these N images are expected to follow Gaussian distribution with the mean of 0 and dispersal of ⁇ 2 as described above.
- the mean value is obtained using the following equation (6).
- the pixel x f for use in the actual calculation of the above equations (6) and (7) for example, only an appropriate pixel x f may be designed to be selected excluding a portion in which air and bone are scanned. When a plurality of pixels are selected, all the obtained values of E[ ⁇ 2 ] are averaged.
- an influence by movement of the subject P may also be designed to be preferably suppressed.
- the risk rate and fidelity are in such a relation that with an increase of one of them, the other also increases.
- the parameter C effectively determines a degree of sensitive reaction of the weight w 1 (p(x,y)) to the risk rate p 1 (x,y). That is, when C is increased, p 1 (x,y) slightly decreases, and w 1 (p(x,y)) approaches 0. Furthermore, when C is reduced, such sensitive reaction can be suppressed.
- the similarity between the center pixel x and peripheral pixel y is judged.
- the rejection of the above-described null hypothesis H concerning both pixels x and y is determined based on the risk rate p 1 (x,y) by a so-called ⁇ square inspection method (statistical inspection method) as apparent from the above.
- a procedure of calculating the risk rate p(x,y) with respect to the respective combinations of x, y and subsequently obtaining the weight w(p(x,y)) does not necessarily have to be executed.
- synthesis function (w o p) may directly be calculated in a constitution.
- the equation (4) can be used to obtain the concrete weight w 1 (p(x,y)) with respect to all the pixels y included in the set N(x) (e.g., the above-described area for 3 ⁇ 3 pixels centering on the pixel x) defined with respect to the certain pixel x. Subsequently, instead of w(p(x,y)) in the equation (2), this w 1 (p(x,y)) can be used to perform the concrete numeric value calculation of the coherent filter.
- FIGS. 3A to 3C This image processing is schematically shown for ease of understanding in FIGS. 3A to 3C . That is, first in FIG. 3A , in 1, 2, . . . , K still images, with respect to the certain pixel x, a rectangular area N 3 ⁇ 3 (x) for 3 ⁇ 3 pixels centering on the pixel x is assumed. Assuming that the pixel in the left corner of the rectangular area N 3 ⁇ 3 (x) is y 1 , the pixel y 1 has a pixel value v(y 1 ).
- a weight w 1 (p(x,y 1 )) is calculated by the above equation (4) ( FIG. 3B ). Furthermore, with respect to the remaining pixels y 2 , . . . y 8 of the rectangular area N 3 ⁇ 3 (x), eventually as shown in FIG. 3B , w 1 (p(x,y 1 )), . . .
- w 1 (p(x,y 8 )), and w 1 (p(x,x)) can similarly be obtained.
- the weights w 1 (p(x,y 1 ), . . . , w 1 (p(x,y 8 )), w 1 (p(x,x)) obtained in this manner are multiplied by the scalar values v k (y 1 ), v k (y 2 ), . . . , v k (y 8 ), v k (x) of the corresponding pixel in the k-th image to obtain a total sum (corresponding to the numerator in the above equation (2)).
- the sum is divided by the sum (similarly corresponding to the denominator of the equation (2)) of the weight w 1 concerning the rectangular area N 3 ⁇ 3 (x).
- the scalar value v′ k (x) with the suppressed noise can be obtained ( FIG. 3C ).
- the K images with the suppressed noise are obtained.
- the above-described steps may be executed, for example, with reference to flowcharts as shown in FIGS. 4A , 4 B.
- the image processing section 110 including the dispersed value estimation section 111 , weight calculation section 112 , and pixel value calculation section 113 may be disposed to execute the steps.
- the weight calculation section 112 is configured to obtain the weight w 1 (p(x,y)) directly from the pixel values v(x) and v(y) as described above. Therefore, the calculation section 112 is an apparatus for directly obtaining the weight without concretely obtaining the value of the risk rate p 1 (x,y). Moreover, instead of the above-described constitution, a constitution may execute two steps of procedure by a risk rate calculation section (fidelity quantization section) for concretely obtaining the value of the risk rate p 1 (x,y), and a weight calculation section for obtaining the weight w 1 (p(x,y)) based on an output of the risk rate calculation section. In any case, the weight calculation section 112 uses the dispersal ⁇ 2 estimated by the dispersed value estimation section 111 , v(x), and v(y) to calculate the weight w 1 (p(x,y)).
- the pixel value calculation section 113 uses the pixel values v(x) and v(y), and the weight w 1 (p(x,y)) whose numeric value is calculated by the weight calculation section 112 to calculate the pixel value v′(x). That is, the calculation section 113 actually executes a step of suppressing the noise of the original image, that is, applies the coherent filter (hereinafter referred to as “the coherent filter is applied”).
- the processing in the image processing section 110 may include: once reconstituting all the still images; subsequently storing the images in the storage apparatus 10 M; and applying the coherent filter to the images as a post processing.
- the present invention is not limited to this mode.
- the step of applying the coherent filter may be carried out in real time (hereinafter referred to as “real time coherent filter processing”).
- the real time coherent filter processing every time a new image is scanned and reconstituted, the following processing is performed.
- the coherent filter can be applied in the same manner as the above-described “dynamic coherent filter processing”.
- the pixel value calculation section 113 calculates only the scalar value v M ′(x) corresponding to the latest image (image number M) instead of calculating all elements of the pixel value v′(x). As a result, since a calculation speed is improved, the latest image with the suppressed noise can be displayed in real time.
- the coherent filter in which only the noise is effectively suppressed without deteriorating the space or time resolution is used to carry out the CBP study, the local blood flow circulations in the tissue, that is, the circulations of the blood flow passed through the capillary in the local tissue is quantitatively analyzed, and the indices (CBP, CBV, MTT, Err) indicating the local blood flow circulations are obtained, so that the enhancement of the precision and reliability can be anticipated.
- the CBP study processing is carried out with respect to the image in which the resolution is inhibited from dropping and the noise is removed.
- the CBP study includes: obtaining indices of CBP, CBV, MTT, and Err quantitatively indicating the circulations of “the blood flow passed through the capillary” in the cerebral tissue; and outputting a map indicating a spatial distribution of these indices:
- CBP blood flow rate [ml/100 ml/min] per unit volume and time in the capillary for the cerebral tissue;
- CBV blood amount [ml/100 ml] per unit volume in the cerebral tissue
- MTT blood mean transit time [second] of the capillary
- a contrast medium having no cerebral vessel permeability such as an iodinated contrast medium
- the iodinated contrast medium rapidly injected via a cubital vein by an injector flows into a cerebral artery via heart and lung. Moreover, the medium flows out to the cerebral vein from the cerebral artery via the capillary in the cerebral tissue.
- the contrast medium having no cerebral vessel permeability, such as the iodinated contrast medium passes through the capillary in a normal cerebral tissue without any extravascular leakage.
- the state of passage of the contrast medium is continuously scanned by a dynamic CT, and a time-density curve Ca(t) of the pixel on the cerebral artery, time-density curve Ci(t) of the pixel on the cerebral tissue including the capillary, and time-density curve Csss(t) of the pixel on the cerebral vein are measured from a continuous image.
- the time-density curve Ca(t) of the cerebral artery blood is used as an input function
- the time-density curve Ci(t) for the cerebral tissue is used as an output function
- characteristics of a process of passage through the capillary can be obtained as a modulation transfer function represented by the rectangular function.
- FIGS. 5 and 6 show a typical procedure of the CBP study according to the present embodiment.
- bolus injection of the vessel such as the cubital vein is performed (the contrast medium is administered at once), and dynamic CT is performed immediately after or before the injection (the same position is repeatedly scanned).
- the scan is repeated, for example, at an interval of 0.5 to 2 seconds for about 20 to 40 seconds.
- a CT number of each pixel (x,y) of a j-th image among N CT images obtained by the dynamic CT is assumed as (x,y,j). This is nothing but a sampled value of a time-density curve (smooth curve) f(t,x,y) in the pixel (x,y).
- the pixels which are apparently judged to correspond to tissues other than the cerebral tissue are excluded from analysis object. That is, the pixel indicating a value outside a range supposed as the CT number for the cerebral tissue (e.g., a CT number of 10 to 60 HU) is a pixel corresponding to air, bone, or fat, is unrelated with a fixed quantity of the cerebral blood flow, and may be negligible.
- This analysis range is set to 10 to 60 HU as default, but can arbitrarily be set via the input section 109 .
- a contrast enhancement effect is initialized.
- the images a plurality of images are generally obtained before the contrast medium reaches the tissue corresponding to each pixel (x,y) are denoted with serial numbers 1, 2, . . . , K, and a time mean value is obtained as follows.
- This q(t,x,y) is used to perform a quantitative analysis of the cerebral blood flow.
- the time-density curves Ca(t) of the cerebral artery of the left brain is used only in analyzing the cerebral tissue of the same left brain.
- the time-density curves Ca(t) of the cerebral artery of the right brain is used only in analyzing the cerebral tissue of the same right brain. This effectively reduces the useless calculation.
- a dividing line is superimposed and displayed as a graphic upon the CT image in a screen (S 3 ).
- the dividing line may first be constituted to be displayed in an image middle. An operator refers to the image, moves the dividing line, moves a plurality of points constituting the dividing line, arbitrarily bends the line, and thereby divides the left and right areas.
- the number of analysis processing steps can be reduced. That is, the time-density curves Ca(t) of the cerebral artery of the left brain (left ACA, MCA, PCA) is used only in analyzing the left brain area (modulation transfer function optimization processing). Similarly, the time-density curves Ca(t) of the cerebral artery of the right brain (right ACA, MCA, PCA) is used only in analyzing the cerebral tissue of the same right brain. To reduce the number of analysis processing steps, the left and right hemispheres are further divided into areas, and the analysis processing may be confined in a much narrower area.
- Voronoy method is a technique for frequent use in a field of optimum arrangement of facilities such as a hospital, shop, and fire station, and is characterized in that a plane is divided into a plurality of areas of influence in accordance with distances from a large number of points (corresponding to the shops, generatrix) disposed on the plane.
- the Voronoy method is separately applied to the left and right hemispheres.
- the left ACA, MCA, PCA are used as three generatrices to divide the left brain area into areas of influence of left ACA, MCA, PCA.
- Voronoy point is set to a center of a circle passed through three generatrices corresponding to the left ACA, MCA, PCA.
- Centering on Voronoy point a perpendicular bisector of two generatrices of the left ACA and MCA, perpendicular bisector of two generatrices of the left MCA and PCA, and perpendicular bisector of two generatrices of the left ACA and PCA are connected to one another.
- the left brain area is divided into three areas of influence by these perpendicular bisectors.
- right ACA, MCA, PCA are used as three generatrices to divide the right brain area into areas of influence of right ACA, MCA, PCA.
- the modulation transfer function MTF of the time-density curve Ci(t) for the cerebral tissue to the time-density curve Ca(t) of the left ACA is confined to the area of influence of the left ACA and obtained for each pixel.
- the modulation transfer function MTF is confined to the area of influence with respect to the left MCA and PCA, and right ACA, MCA, PCA, and obtained for each pixel.
- the number of analysis processing steps can further be reduced.
- a cerebral artery ROI is set on the cerebral artery on the CT image.
- the ROI setting support section 121 prepares a support map, and the map is displayed separately from or upon the CT image (S 4 ).
- examples of the support map includes an appearance time (AT) map, peak time (PT) map, and transit time (TT) map. With respect to the respective pixels, as shown in FIG.
- time AT from an arbitrary time T 0 before the contrast imaging (e.g., data collection start time) until a contrast medium concentration reaches several percents (e.g., 1%) of a peak
- time (peak time) PT from the time T 0 until the contrast medium concentration reaches the peak
- TT indicating a movement time of the contrast medium, for example, with a half value width is calculated, and generated and displayed as the map.
- all types including these AT, PT, and TT maps are generated and displayed, but an operator can select arbitrary one type or two types.
- the cerebral artery ROT is set to three places of the anterior cerebral artery (ACA), medial cerebral artery (MCA), and posterior cerebral artery (PCA).
- ACA anterior cerebral artery
- MCA medial cerebral artery
- PCA posterior cerebral artery
- the setting of the individual cerebral artery ROIs for the respective slices is not only large in an operation burden but also an unnecessary operation in performing the analysis. Therefore, the cerebral artery ROT set in a certain arbitrary one slice is also used in other slices. Moreover, a coherent regression method described later may also be used to prepare the time-density curve Ca(t) of the cerebral artery which can be used in common to all the slices.
- the time-density curve preparation section 122 prepares the time-density curve Ca(t) from continuous image data by dynamic CT with respect to each set cerebral artery ROT (S 6 ).
- any pixel on the image does not correctly indicate the CT number of artery blood, one pixel is constituted by mixed presence of the cerebral artery and other tissues, and only a lower contrast enhancement effect is indicated because of a partial volume effect in most cases.
- an image noise is large.
- the contrast enhancement effect is remarkably small in the artery of a portion with cerebral infarction caused therein, the influence of noise is enormously large.
- the image noise is suppressed by the above-described coherent filter, but the influence of the partial volume effect still remains.
- the pixels in a solid including the artery are used to apply the coherent regression method described later, so that the problem can be solved. Therefore, instead of the above-described coherent filter method, the coherent regression method may also be applied in this stage.
- the time-density curve of only one slice image corresponding to each artery is obtained, and therefore the curve can be used in analyzing the arbitrary portion in all the slices within the scan volume.
- the slice by which the time-density curve of the cerebral artery is most clearly obtained is selected, the time-density curve of the cerebral artery can be applied to all the slices, and the number of time-density curves of the cerebral artery can be reduced.
- the “time-density curve” is a curve indicating a change of the CT number (density value) in the specific portion of the dynamic CT image with elapse of time.
- the change of the contrast medium concentration in the specific tissue of the human body with time has been measured as the time-density curve.
- the time-density curve is used. The curve will more formally and clearly be described.
- an absolute value of d k is not necessarily required, and it is rather sufficient to obtain only an increment (d k ⁇ d 1 ) in which the first image 1 is used as a reference.
- the dynamic CT image scanned by the medical image diagnosis apparatus includes the random noise, and therefore there is a problem that the time-density curve essentially to be measured cannot correctly be obtained.
- the time or spatial smoothing has heretofore been used to suppress the random noise.
- time average the time resolution is impaired.
- space averaging there is a problem that the change with time of the density of the portion other than the portion essentially to be measured is mixed in the measured value.
- the coherent filter is used.
- a set R of the pixels substantially corresponding to the portion to be measured is set.
- p(x) and q(x) are unknown coefficients which differ with each pixel x but do not change depending on an image number k (i.e., scan time t k ), and are modeled partial volume effects.
- ⁇ k (x) is a modeled random noise, the value differs with each pixel x and image number k, but the anticipated value is 0, and the statistic distribution does not depend on the pixel x or the image number k.
- a 1 and a 2 are unknown coefficients which differ with each pixel set x, y but do not change depending on the image number k (i.e., the scan time t k ).
- ⁇ k is a random noise, the value differs with each pixel set x, y and image number k, but the anticipated value is 0.
- v k ⁇ ( x ) p ⁇ ( x ) p ⁇ ( y ) ⁇ v k ⁇ ( y ) + ( q ⁇ ( x ) - p ⁇ ( x ) p ⁇ ( y ) ⁇ q ⁇ ( y ) ) + ( ⁇ k ⁇ ( x ) - p ⁇ ( x ) p ⁇ ( y ) ⁇ k ⁇ ( y ) ) ( 15 ) Therefore, with the following equation, the equation (12) is derived.
- a 1 and a 2 of the equation (16) are parameters indicating the partial volume effect
- ⁇ k Of the equation (16) indicates a random noise.
- the equation (17) is quickly derived from the equation (16) indicating the definitions of a 1 and ⁇ k , and general properties of the dispersal concerning a random variable. Moreover, the value of the above-described dispersal ⁇ 2 can simply be estimated sufficiently for practical use.
- a known fitting method can be used as such in calculating the optimum estimated values of the constants a 1 and a 2 . Then, as a typical concrete method of the fitting method, an outline in the use of a linear minimum square method will be described. To apply the linear minimum square method to the present embodiment, assuming that simply the square sum Of ⁇ k in the null hypothesis is S(a), the following is defined.
- the present embodiment is one modification example of the coherent filter.
- the f(a ⁇ tilde over ( ) ⁇ ,v(y)) means that the parameter a indicating the partial volume effect is adjusted to be optimum and the pixel value v(y) of the pixel y is converted so as to have a highest fidelity with the pixel value v(x) of the pixel x.
- a method of obtaining the time-density curve using the null hypothesis H 0 ′′ by the coherent filter in the present embodiment will next be described.
- v ′ ⁇ ( x ) ⁇ y ⁇ R ⁇ ⁇ w ( p ⁇ ( x , y ) ⁇ f ⁇ ( a ⁇ , - v ⁇ ( y ) ) ⁇ y ⁇ R ⁇ ⁇ w ⁇ ( p ⁇ ( x , y ) ) ( 22 )
- the time-density curve obtained in this manner indicates a measured value which approximates primary conversion ⁇ t k ,A(d k ⁇ d 1 )> ⁇ (wherein A is an unknown coefficient) of the true time-density curve in the pixel x ⁇ t k ,d k > ⁇ .
- A is an unknown coefficient
- the random noise is suppressed by the effect of the weighted mean.
- the curve in which the influence of the partial volume effect is corrected is used.
- the present invention has the common characteristic of the coherent filter “the time mean is not used, and the space mean is calculated using the weight based on the fidelity with the pixel x” as a property.
- the time-density curve can be obtained in which the influence of the partial volume effect is suppressed without impairing the time resolution and the random noise is suppressed. Additionally, a method of obtaining the time-density curve in this manner is referred to particularly as the “coherent regression method”.
- the dynamic CT image obtained by the dynamic CT scan in medical X-ray CT One example of clinical use of the time-density curve will next concretely be described in the dynamic CT image obtained by the dynamic CT scan in medical X-ray CT.
- the scan such as dynamic CT is performed, the density change of the image of the artery existing in the human body tissue is measured as the time-density curve, and the blood flow circulation in the tissue is diagnosed.
- This measured value contains the random noise.
- the coefficient A remains to be unknown.
- the area under curve AUC(d) of the time-density curve ⁇ t k ,(d k ⁇ d 1 )> concerning the certain vessel d can approximately be calculated, for example, by the following equation.
- the area under curve AUC(J) concerning the time-density curve ⁇ t k ,(J k ⁇ J 1 )> ⁇ obtained with respect to the vein in the conventional method can be calculated using the equation (22). J may be assigned to d. Moreover, if the time-density curve ⁇ t k ,(D k ⁇ D 1 )> ⁇ is known with respect to the artery, the area under curve AUC(D) can similarly be calculated using the equation (18). Additionally, according to the proposition S, the following must be established. AUC ( D ) ⁇ AUC ( J ) (24) However, in actual, since the time-density curve ⁇ t k ,(D k ⁇ D 1 )> ⁇ is unknown, AUC(D) cannot be calculated.
- the time-density curve ⁇ t k ,(v′ k (x) ⁇ v′ 1 (x))> obtained in the method according to the present embodiment approximates ⁇ t k ,A(D k ⁇ D 1 )>, and the latter contains the unknown coefficient A. Therefore, an area under curve AUC(v′) which can concretely be calculated from ⁇ t k ,(v′ k (x) ⁇ v′ 1 (x))> ⁇ using the equation (23) has to be just A times the area AUC(D). That is, the following results.
- a ⁇ AUC ( v ′)/ AUC ( J ) (26) The right side of the equation (26) can concretely be calculated using the equation (23), and therefore the value of the coefficient A which has been unknown can concretely be determined. Then, when this value of the coefficient A is used to constitute the time-density curve ⁇ t k ,(v′ k (x) ⁇ v′ 1 (x))/A>, this is nothing but approximation of the time-density curve ⁇ t k ,(D k ⁇ D 1 )> of the artery.
- a method of using the area under curve to constitute the time-density curve having the determined value of the proportional coefficient A which has been unknown is referred to as an “AUC method”.
- the AUC method is further combined with the coherent regression method in the clinical use of the time-density curve in the dynamic CT image obtained by the dynamic CT scan, thereby the influences of the partial volume effect and random noise are removed, and the measured value including no unknown proportional coefficient A is obtained even with respect to the time-density curve of a thin artery.
- the measurement of the curve has been difficult or impossible in the conventional method.
- the AUC method can also be applied to the time-density curve ⁇ t k ,(v′ k (x) ⁇ v′ 1 (x))> concerning the artery singly measured by the conventional method.
- the influences of the random noise and partial volume effect cannot be removed, but the time-density curve having the determined value of the proportional coefficient A which has been unknown can be constituted.
- the time-density curve Csss(t) of the upper sagittal sinus venosus may be used to correct the time-density curve Ca(t) of the cerebral artery.
- a slightly large upper sagittal sinus venosus ROI is set so as to surround the upper sagittal sinus venosus on the CT image. Since the upper sagittal sinus venosus is large as compared with the artery and the position thereof is relatively fixed, it is easy to set the upper sagittal sinus venosus ROI.
- This slightly large upper sagittal sinus venosus ROI includes a plurality of pixels.
- the upper sagittal sinus venosus ROI is reduced/processed so that all the pixels of the upper sagittal sinus venosus ROI are included in the upper sagittal sinus venosus over the whole area (S 8 ).
- the reduction processing includes: first executing a threshold value processing (binarization) with respect to each of the pixels in the upper sagittal sinus venosus ROI; and preparing a binary map in the ROI (“0”, “1”).
- the threshold value is set to a value which separates the image of the upper sagittal sinus venosus from the image of the peripheral tissue and bone.
- “1” indicates the pixel on the image of the upper sagittal sinus venosus
- “0” indicates the pixel on the image of the peripheral tissue and blood.
- Each pixel (center pixel) of the binary map is replaced in accordance with the values of four or eight pixels in the vicinity. Only when the center pixel is “1”, and all the four or eight pixels in the vicinity are “1”, the value of the center pixel is maintained at “1”. That is, of course when the center pixel is “1”, even when the pixel is “1”, and also when any one of the four or eight pixels in the vicinity indicates “0”, the value of the center pixel is replaced with “0”.
- the upper sagittal sinus venosus ROI is reduced by at least one pixel as compared with the outer shape of the image of the upper sagittal sinus venosus.
- the area under curve AUC of the time-density curve may be used to correct the upper sagittal sinus venosus ROI.
- the slightly large ROI is used as a search range, and the area under curve AUC of the time-density curve is calculated with respect to each of the pixels in the range.
- the area under curve AUC of the pixel on the upper sagittal sinus venosus image apparently indicates a high value as compared with the value of the peripheral pixel. Therefore, when the threshold value processing is executed with respect to the area under curve AUC, only the pixel on the upper sagittal sinus venosus image can be selected from the ROI.
- the time-density curve of each pixel is averaged, and the time-density curve Csss(t) of the upper sagittal sinus venosus is prepared (S 9 ).
- the iodinated contrast medium does not pass through a blood brain barrier, in principle, iodine concentration does not change with the cerebral artery and vein. That is, the area under curve AUC of the time-density curve Csss(t) of the upper sagittal sinus venosus is almost equivalent to the area under curve AUC of the time-density curve Ca(t) of the cerebral artery prepared in S 6 . Therefore, as shown in FIG.
- the time-density curve Ca(t) is corrected by multiplying each time value of the time-density curve Ca(t) of the cerebral artery prepared in S 6 by AUC(sss/AUCa) so that the area under curve AUCa of the time-density curve Ca(t) of the cerebral artery prepared in S 6 is almost equivalent to the area under curve AUCsss of the time-density curve Csss(t) of the upper sagittal sinus venosus (S 10 ).
- the time-density curve Ca(t) of the cerebral artery shown in FIG. 14A in which the noise and partial volume effect are suppressed as described above is used to quantize the state of the blood flow circulation for the cerebral tissue (capillary).
- the time-density curve Ci(t) shown in FIG. 14B is first prepared with respect to each pixel on the cerebral tissue (S 11 ).
- the separate cerebral artery time-density curves Ca(t) are used for the left and right areas, and the cerebral artery time-density curve Ca(t) is used as the input function and the time-density curve Ci(t) for the cerebral tissue is used as the output function for each pixel to obtain the characteristics of process of passage of the tracer through the capillary as the modulation transfer function MTF. That is, with respect to the time-density curve Ci(t) for the cerebral tissue of the left area, the time-density curve Ca(t) of the cerebral artery of the same area is used.
- the time-density curve Ca(t) of the cerebral artery of the same right area is used to obtain the modulation transfer function MTF. Furthermore, since the cerebral artery time-density curve Ca(t) is prepared for each of ACA, MCA, PCA as described above, the calculation of the modulation transfer function MTF is repeated every Ca(t).
- FIG. 16 shows a principle of the box-MTF method.
- the method includes: evaluating a residual errors error between a convolution Ci′(t) of the time-density curve Ca(t) of the cerebral artery with a modulation transfer function box-MTF represented by a rectangular function and actual measurement Ci(t) prepared in S 11 ; and correcting the modulation transfer function box-MTF so as to reduce a square sum of the residual errors error. This procedure routine is repeated to minimize the residual errors error.
- CBP, CBV, MTT are calculated based on the modulation transfer function box-MTF which minimizes the residual errors error (S 13 ), and the square sum of the residual errors error minimized in S 12 is output as Err. Strictly, the correction is performed with the following.
- MTT (1 ⁇ Ht )/(1 ⁇ b*Ht )* MTT′
- Ht is a hematocrit value of a major vessel
- b*Ht is a hematocrit value of a peripheral vessel (generally b is about 0.7).
- the residual errors error is given by y i (x) ⁇ f(t i ,x).
- y i (x) indicates the scalar value of a box cell x in time t i , and corresponds to the time-density curve for the cerebral tissue.
- f(t i ,x) indicates the scalar value in the time t i of a model fitted to the vector pixel value of the box cell x, and corresponds to the convolution of the modulation transfer function with the time-density curve of the cerebral artery.
- Err is a square root of the square sum of the residual errors error in approximating the modulation transfer function, and calculated, for example, as represented by the following equation.
- p denotes a degree of freedom, that is, the number of parameters included in an approximated model f.
- w(t i ) is a weight coefficient which determines a degree of contribution of the residual errors error in the time t i to Err.
- w(t i ) does not have to depend on i, and may have a fixed value such as 1.
- w(t i ) ⁇ e ⁇ ti2/ ⁇ is also acceptable which is constituted so that the weight w moderately decreases with an increase of
- the respective maps are generated from CBP, CBV, MTT, Err subjected to output optimization (S 16 ).
- the maps increase to the number four times the increase number of arteries. It is not realistic to generally evaluate such many maps.
- the maps are synthesized (S 17 ).
- synthesis method includes: synthesizing the CBP maps of the anterior cerebral artery ACA, medial cerebral artery MCA, and posterior cerebral artery PCA based on the residual errors Err of anterior cerebral artery ACA, medial cerebral artery MCA, and posterior cerebral artery PCA.
- the modulation transfer function MTF is obtained from the time-density curve Ca(t) of the anterior cerebral artery ACA and the time-density curve Ci(t) for the cerebral tissue under the control
- the residual errors error Err is relatively small.
- the modulation transfer function MTF is obtained from the time-density curve Ci(t) for the cerebral tissue not under the control
- the residual errors error Err is relatively large. That is, the residual errors error Err indicates a control possibility of each cerebral artery.
- the CBP value corresponding to a lowest value of residual errors error Err is selected as the value of the pixel from the CBP values of the anterior cerebral artery ACA, medial cerebral artery MCA, and posterior cerebral artery PCA.
- the map synthesized in this manner is constituted of the CBP value for the cerebral tissue having a high possibility of being under the control of the anterior cerebral artery ACA, medial cerebral artery MCA, and posterior cerebral artery PCA. This also applies to the map synthesis of the other indices CBV, MTT.
- the time-density curve obtained from the pixel existing in the position corresponding to the artery reflects a contrast medium concentration in artery blood, and the above-described coherent regression method is applied, so that the time-density curve of a correct artery blood contrast medium concentration can be obtained.
- Such time-density curve of the cerebral artery can be prepared for each artery, and differs depending on a blood circulation state. Particularly, in a case of cerebral vascular disorder, the difference is sometimes remarkable.
- the image can be constituted with the value as the pixel value, and this image is an index map.
- R types typically four types of CBP, CBV, MTT, Err as described above
- R maps can be constituted.
- R maps prepared in this manner can be regarded as one map (vector value map) in which each pixel has a vector value. That is, the following results.
- V k ⁇ ( x , y , z ) ⁇ P k , 1 ⁇ ( x , y , z ) , P k , 2 ⁇ ( x , y , z ) , ... ⁇ , P k , R ⁇ ( x , y , z ) >
- P k,1 (x,y,z) can be constituted to indicate the value of CBP
- P k,2 (x,y,z) to indicate the value of CBV
- P k,3 (x,y,z) to indicate the value of MTT
- P k,4 (x,y,z) to indicate the value of residual errors error Err.
- a portion apparently not corresponding to an internal organ as the analysis object is excluded from the analysis object from the beginning, and a special value indicating the exclusion from the analysis object may be assigned to P k,r (x,y) (the steps S 14 , S 15 ).
- P k,r the steps S 14 , S 15 .
- a negative value whose absolute value is large as the value is convenient.
- the time-density curve of the cerebral artery obtained from the artery in a right hemisphere has to be used only in analyzing the portion (x,y,z) belonging to the right hemisphere
- the time-density curve of the cerebral artery obtained from the artery in a left hemisphere has to be used only in analyzing the portion (x,y,z) belonging to the left hemisphere.
- an operator designates a boundary (median line) of the right and left hemispheres as a line, curve, bent line, plane, or curved surface, so that the map is preferably prepared for each hemisphere in the constitution.
- P k,R (x,y,z) is the residual errors error map
- V(x,y,z) V k (x,y,z)
- k is such that
- is minimized among k 1, 2, . . . , K.
- a map P 0 (x,y,z) (k such that
- R or R+1 images may be observed.
- V k (x,y,z) is originally similar to V j (x,y,z) in the portion (x,y,z), and there is hardly possibility that a mistake is made in interpreting V(x,y,z) by this mistake.
- the region of interest ROI including a plurality of pixels is set with respect to the map synthesized as described above, or the single CBP, CBV, MTT, or Err map in each cerebral artery (S 18 ), mean values (CBP, CBV, MTT, Err mean values) of the pixel values (CBP, CBV, MTT, Err values) in the ROI are calculated (S 19 ), and the mean value is sometimes used as a diagnosis material.
- the ROI can be used in common to the other maps.
- An ROI setting operation is simplified, and it is also possible to calculate the mean value concerning the same ROT (CBP, CBV, MTT, Err mean values).
- the minimum residual errors error Err of the time-density curve of the certain tissue with respect to the time-density curve of the certain cerebral artery indicates a degree of control in the tissue by the cerebral artery, that is, a degree of blood flow supply to the tissue by the cerebral artery.
- the error indicates a degree in the tissue belonging to the cerebral artery, that is, a degree of blood flow supply to the cerebral tissue from the cerebral artery.
- the cerebral artery corresponding to the small residual errors error Err indicates a high control possibility with respect to the cerebral tissue of the pixel, and the cerebral artery corresponding to a large residual errors error Err indicates a low control possibility with respect to the cerebral tissue of the pixel.
- the residual errors Err of the anterior cerebral artery ACA, medial cerebral artery MCA, and posterior cerebral artery PCA are compared with one another for each pixel. It is indicated that the cerebral artery (ACA, MCA, or PCA) indicating a minimum residual errors error has a highest possibility of controlling the cerebral tissue of the pixel. For each pixel, the cerebral artery having the highest control possibility, that is, the minimum value of the residual errors error Err is specified. A label corresponding to the specified cerebral artery is given to each pixel.
- FIG. 23 shows an example of a generated control map.
- the label is distinguished and displayed with color and shading.
- the index map is filtered with the arbitrary label, as shown in FIGS. 24A , 24 B, 24 C, it is possible to extract the region having the high control possibility from the index map for each cerebral artery (ACA, MCA, or PCA).
- the coherent filter or coherent regression by the coherent filter or coherent regression, the space and time resolutions are inhibited from dropping, and the noise is suppressed, so that the analysis precision of the CBP study can be enhanced.
Abstract
Description
V k(x,y,z)=<P k,1(x,y,z), P k,2(x,y,z), . . . , P k,R(x,y,z)>
v(x)=(v 1(x), v 2(x), . . . , v K(x)) (1)
wherein v1(x), v2(x), . . . , vK(x) in the right side of the equation (1) will hereinafter be referred to as “scalar values” with respect to the pixel x.
wherein k=1, 2, . . . , K. Subsequently v′k(x) obtained by this equation is used to constitute a converted pixel value (new pixel value) v′(x) of the pixel x as follows.
v′(x)=(v′ 1(x), v′ 2(x), . . . , v′ K(x)) (3)
v(x)=(v 1(x), v 2(x), . . . , v K(x)) (1)
Here, suffixes 1, 2, . . . , K in right-side terms are serial numerals of K still images.
-
- wherein yεN(x), and this set N(x) may arbitrarily be set with respect to the pixel x (=may also be set by any standard). However, in actual, a possibility of satisfying the hypothesis “v(x)=v(y), where a difference resulting from the noise of both pixels is removed” by the pixel x and the pixel y disposed apart from the pixel x can be the to be generally low. Therefore, to limit the set N(x) on an assumption that the set N(x) is a set of pixels disposed in the vicinity of the pixel x has a practical significances such as improvement of a calculation speed.
Then, an anticipated value E[σ2] can be obtained with respect to the true dispersal σ2 as follows.
Moreover, it can be considered that the anticipated value E[σ2] of the dispersal is proper with respect to all the pixels x on all the K still images as described above. A likelihood of the anticipated value is guaranteed for use as a substitute for the true dispersal σ2 by not less than a constant degree. Therefore, in the actual calculation of the above equation (4), this E[σ2] may be assigned to σ2 of the equation (4).
Moreover, the above equation (4) is converted to the following with respect to p1(x,y) represented in the equation (8).
wherein A is a constant standardized so that p1 indicates a value of (0 to 1).
q(x,y,j)=v(x,y,j)−b(x,y)
With j<K, the following may be set.
q(x,y,j)=0
v k(x)=p(x)d k +q(x)+γk(x) (11)
(k=1, 2, . . . , K)
v k(x)=a 1 v k(y)+a 2+ξk (k=1, 2, . . . , K) (12)
v k(y)=p(y)d k +q(y)+γk(y) (13)
That is, when the above equation obtained by assigning y to x is modified the following equation is obtained.
When this is assigned to equation (20), the following is obtained.
Therefore, with the following equation, the equation (12) is derived.
Here, a1 and a2 of the equation (16) are parameters indicating the partial volume effect, and ξk Of the equation (16) indicates a random noise.
h(a 1)=1+a 1 2 (17)
The equation (17) is quickly derived from the equation (16) indicating the definitions of a1 and ξk, and general properties of the dispersal concerning a random variable. Moreover, the value of the above-described dispersal σ2 can simply be estimated sufficiently for practical use.
The value of S(a) depends on a constant vector a=(a1,a2), that is, the values of the constants a1 and a2. With calculation of the constant vector a in which S(a) indicates the minimum value, the optimum estimated values a1{tilde over ( )} and a2{tilde over ( )} can be obtained with respect to the constants a1 and a2 in the meaning of an unbiased estimate. Furthermore, as a concrete calculation method of the linear minimum square method, various known methods can be used. In addition, these known calculation methods are all very simple, and required calculation time is very small.
r k{tilde over ( )}(x,y)=v K(x)−a 1 {tilde over ( )}v k(y)−a2{tilde over ( )} (19)
Therefore, this residual errors error rk{tilde over ( )} can be used to rephrase the above-described null hypothesis H0′ as a substantially equivalent null hypothesis H0″ “rk{tilde over ( )}(x,y) (k=1, 2, . . . , K) follows a normal distribution with a mean of 0 and dispersal of (1+(a1{tilde over ( )})2)σ2”. This is a concrete proposition by which verification calculation can actually be executed.
wherein the vectors a and ξ depend on the set of pixels
x,y·f(a{tilde over ( )},v(y))=a 1 {tilde over ( )}v(y)+a 2{tilde over ( )} (21)
Moreover, a vector value function f defined by the above equation is used to rephrase the null hypothesis H0′ as the null hypothesis H0″ “v(x)=f(a{tilde over ( )},v(y))+ξ (however, ξ follows a normal distribution with a mean of 0 and dispersal of (1+(a1{tilde over ( )})2)σ2)”, and this is the same form as that of the above-described null hypothesis H0. That is, it is apparent that the present embodiment is one modification example of the coherent filter. Here, the f(a{tilde over ( )},v(y)) means that the parameter a indicating the partial volume effect is adjusted to be optimum and the pixel value v(y) of the pixel y is converted so as to have a highest fidelity with the pixel value v(x) of the pixel x.
AUC(D)≅AUC(J) (24)
However, in actual, since the time-density curve {<tk,(Dk−D1)>} is unknown, AUC(D) cannot be calculated.
AUC(v′)≅A AUC(D) (25)
That is, from the equations (24) and (25), the following relation is established.
A≅AUC(v′)/AUC(J) (26)
The right side of the equation (26) can concretely be calculated using the equation (23), and therefore the value of the coefficient A which has been unknown can concretely be determined. Then, when this value of the coefficient A is used to constitute the time-density curve <tk,(v′k(x)−v′1(x))/A>, this is nothing but approximation of the time-density curve <tk,(Dk−D1)> of the artery. A method of using the area under curve to constitute the time-density curve having the determined value of the proportional coefficient A which has been unknown is referred to as an “AUC method”.
CBP=CBP
CBV=(1−Ht)/(1−b*Ht)*CBV′
MTT=(1−Ht)/(1−b*Ht)*MTT′
Here, Ht is a hematocrit value of a major vessel, and b*Ht is a hematocrit value of a peripheral vessel (generally b is about 0.7).
Claims (14)
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Also Published As
Publication number | Publication date |
---|---|
CN1236732C (en) | 2006-01-18 |
CN1682660A (en) | 2005-10-19 |
US7826885B2 (en) | 2010-11-02 |
EP1302163A2 (en) | 2003-04-16 |
EP1302163A3 (en) | 2003-11-19 |
CN100379385C (en) | 2008-04-09 |
US20080075344A1 (en) | 2008-03-27 |
EP1302163B1 (en) | 2006-07-05 |
US20030097076A1 (en) | 2003-05-22 |
CN1413559A (en) | 2003-04-30 |
DE60212917D1 (en) | 2006-08-17 |
DE60212917T2 (en) | 2007-03-01 |
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